{"paper":{"title":"Quasilinear elliptic Hamilton-Jacobi equations on complete manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Laurent Veron (LMPT), Marie-Fran\\c{c}oise Bidaut-Veron (LMPT), Marta Garcia-Huidobro","submitted_at":"2013-05-29T08:37:55Z","abstract_excerpt":"Let (M^n,g) be a n-dimensional complete, non-compact and connected Riemannian manifold, with Ricci tensor Ricc_g and sectional curvature Sec_g. Assume Ricc_g\\geq (1-n)B^2, and either p>2 and Sec_g(x)=o(dist^2(x,a)) when dist^2(x,a)\\to\\infty for a\\in M, or 1<p<2 and Sec_g(x)\\leq 0. If q>p-1> 0, any C^1 solution of (E) -\\Gd_pu+\\abs{\\nabla u}^q=0 on M satisfies \\abs{\\nabla u(x)}\\leq c_{n,p,q}B^{\\frac{1}{q+1-p}} for some constant c_{n,p,q}>0. As a consequence there exists c_{n,p}>0 such that any positive p-harmonic function v on M satisfies v(a)e^{-c_{n,p}B\\dist (x,a)}\\leq v(x)\\leq v(a)e^{c_{n,p}B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6720","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}